Math
Sigma notation.
Definition
A compact way to write the sum of a sequence of terms using the Greek letter Σ (sigma). It specifies a formula for each term, a starting index, and an ending index. For example, Σ from i=1 to n of aᵢ means a₁ + a₂ + ... + aₙ.
Examples
Real-world.
- 1 Σ from i=1 to 5 of i = 1 + 2 + 3 + 4 + 5 = 15
- 2 Σ from k=1 to 4 of k² = 1 + 4 + 9 + 16 = 30
- 3 Writing Riemann sums in compact form using sigma notation
Key Fact
Σ from i=1 to n of i = n(n+1)/2